General approaches and asymptotic methods of the theory of collisions of atomic particles are presented . Asymptotic methods of calculating the potentials of exchange interaction of atomic particles at long distances responsible for transitions during collisions of atomic particles are considered, the results for specific transitions are presented. Dynamics of inelastic collision of slow atoms, ions, molecules is analyzed, general methods of separation of transition channels and finding transition probability amplitudes in a quasi-classical approximation are developed. The general results are used for the theoretical analysis of three groups of collision processes of atoms, ions and molecules: resonant processes, quasi-resonance processes, collision processes with the transition to a continuous and quasi-neural spectrum. The results of the theory are compared with experimental data ..